Before I get into the heart of the presentation, I would like to thank my two amazingly talented students who lead all of this work, ChatGPT browser tab 2 and Claude browser tab 3.
#fundingcuts #academia
Bees on the 2D simplex. Which simplex do we choose?
Bees on the 1D simplex
Round 2 of collective decision making as a feedback control problem. This time we visit the Seeley model. How do bees avoid deadlock and obstructions to stabilization? To control engineers need to practice headbutting?
hackmd.io/yTBuClZ0Sh65...
Asked my PDE neighbor on how I could solve a regularity problem I bumped into, and they responded with suggestions of prompts I could try punching into chatgpt
:/
Latest blog post of clopenloop is coincidentally on how the generative modeling method of flow matching can be used to go from open loop trajectories to closed loop based feedback synthesis.
t.co/q0InluvTWy
Had the nice opportunity to visit University of California, San Diego, to spread some transport for nonlinear systems propaganda: tinyurl.com/2mfdpj66
A highlight of the trip was seeing Do Ho Suh’s incredible artwork, Fallen Star perched on the school of engineering building. tinyurl.com/4ufrnvz5
The inverted pendulum is steered to its Sisyphean headstand once more. But without eigenvalues, Lyapunov, or bribery. Instead, using denoising as a control steering mechanism.
Latest post on generative modeling for control: hackmd.io/kjV3PiI4ROOP...
The Fall from the Ivory Tree
An essay on the despair of the academic job cycle,
and the hope that must follow -
hackmd.io/@clopenloop/...
Link to my zoom talk at the GERAD Research Center, "A Transport Theoretic Perspective for Nonlinear Control":
www.youtube.com/watch?v=cXy1...
Thanks to the organizers, Aditya Mahajan, Peter Caines, and Shuang Gao for the wonderful opportunity to present and great interactions.
The generative modeling for control lectures are proceeding in nonlinear order. Here is one on a control generalization of gradient descent that I refer to as nonholonomic gradient descent. I explain why it's doomed to fail due to Brockett, and how noise might save us.
hackmd.io/pTtk6ohHSBSf...
Encoding geometry in neural network architectures has wide applications, from robots' configuration spaces to safety. We present natural ways to enforce constraints by design.
Link to preprint: www.researchgate.net/publication/...
#geometricdeeplearning
Designing the optimal slide for a lion, of course.
Also curious if you are going to be rightfully referring to the maximum principle as the Pontryagin–Boltyanskii–Gamkrelidze–Mishchenko Maximum Principle it time you mention it. 😆
What is a good source for this? And is there a non-finance analogue of arbitrage opportunities that motivates this?
All hail the Lie bracket 🙌
I’m writing notes on how generative modeling connects with control theory.
Starting with intuition: simulations, nonlinear control, and how stochastic dynamics can shape long-term behavior.
LN1 (Fokker–Planck): hackmd.io/@clopenloop/...
LN2 (Nonholonomic Fokker-Planck): hackmd.io/@clopenloop/...
The road to the maximum principle turns out to be more non-smooth than one might expect.
Boltyanski, Martini & Soltan’s book ( Geometric Methods and Optimization Problems) has far more drama than you’d guess from the Sussmann–Willems survey.
Job season in academia can take a toll on confidence, identity, and energy. You’re not alone.
Sometimes it helps to zoom out.
Hunter Wapman’s thesis highlights some interesting hiring patterns:
www.hne.golf/static/pdfs/...
Non-US trends may differ, perhaps shaping distinct knowledge bubbles.
I suspect a case of chaos or non-uniqueness. 🧐
Multi-agent control often feels like control theorists doing dynamical systems instead of control theory. What if we posed it like classic control problems.
Collective decision-making as feedback stabilizability. Turns out, it leads to a strange kind of control problem.
hackmd.io/@clopenloop/...
It’s hard enough following Stroock when he’s explaining his own perspective.😵💫
A basin of attraction
An interesting result on how LQ problems in optimal control can fail to have minimizers: arxiv.org/pdf/1311.200... (in an almost merciless way).
Naive random sampling of initial conditions and control.
Optimal Transport (OT) is emerging as a versatile tool for control questions. We show an OT-based way to sample from the reachable set (RS), especially useful when systems have strong attractors.
www.researchgate.net/publication/...
RS of Van der Pol vs. naive random sampling (below).
Finally, my YouTube debut! A recording of my talk at the AI and data seminar series organized by the Automatic Control Engineering Network.
m.youtube.com/watch?v=o-4B...
Here I pontificate on using time reversals of diffusions for stabilization and planning problems.
I am starting to compile some notes on Generative Modeling for Control Theory. The goal is to include topics such as degenerate Fokker-Planck equations (FPEs) and Optimal transport theory. Here is a first post on the classical (nicer) FPE and its long-term behavior.
hackmd.io/@clopenloop/...
That’s an amazing stat 😵
